Buying Filberts On a Sample Basis
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1 E 55 m ^7q Buying Filberts On a Sample Basis Special Report 279 September 1969 Cooperative Extension Service c, 789/0 ite IP") 0, i mi 1910 S R e, `g,,ttsoliktill:torvti EARs srin ITQ, E,6 </ Oregon State University Corvallis
2 Buying Filberts on a Sample Basis Introduction and Background Oregon filberts are traded between grower and handler on the basis of a sample. The sample is a small quantity of filberts taken at the time of delivery and is used as a basis to determine price per pound to the grower. Price is determined on size of nuts, moisture content, crack test, and worm content. Although all plants in Oregon use a sampling procedure for determining final price paid to the grower, the size of sample and method used for selecting the sample varies among plants. In addition to this variation, some plants pay on a green weight basis and some on a dry weight basis. Each has its advantages and disadvantages to the growers and handlers. One of the key points for controversy relates to the confidence growers have in the ability of a sample to predict the proportion of saleable filberts in a lot. The handler is concerned that he not only receives what he pays for, but that he can also assure the grower's satisfaction. Perhaps one of the greatest advantages of sample buying is that it permits the handler to receive filberts from more than one grower at the same time. It permits continuous operation of the drying and packing lines and permits the handler to mix lots, thus eliminating the need to keep each lot separate. Buying on a green weight basis has even greater advantages because drying space can be used at a maximum capacity and kept full at all times. When buying on a green weight basis, the moisture content is determined by a Steinlite Moisture Tester using a 50-gram sample in nearly all cases. Prepared by: Roland H. Groder, Fruit and Vegetable Marketing Specialist, Lyle D. Calvin, Head,Statistics Department, and Helen Lowry, Assistant-in-Statistics.
3 -2- Recommendations: Oregon State University had an opportunity to evaluate the sampling procedures used by one of the firms in 1967 and arrived at the following recommendations to the filbert industry that: 1. Some mechanical means be used to draw a random sample from each ton of nuts delivered. This will eliminate the possibility of human bias in the selection of nuts. 2. The size of each sample be large enough to supply 50 nuts for a crack test and 50 grams of nuts for a moisture test. 3. The Steinlite Tester be properly calibrated and operated by a trained operator. The tester is accurate enough in determining moisture content to permit buying nuts on a green weight basis. 4. Size factors be eliminated from the buying and paying formula because price can be estimated with satisfactory precision without sizing the samples. 5. Total weight, percent blanks, and percent moisture of green nuts be used as a basis for determining payment to the growers. 6. In determining the payment to growers, a minimum of seven random samples of 50 nuts plus 50 grams be drawn from each lot of nuts to achieve a 90 percent confidence level of ± four percent. Assumptions: The analysis and conclusion reached are based on certain assumptions. These assumptions are an important consideration for proper interpretations and must be kept in mind when studying or reading this report. The assumptions are as follows: 1. That filberts are well mixed in each lot or that sampling is completely at random.
4 -3-2. That any bias in converting from a dry to a green weight basis can be adjusted for either in the initial payment or through rebate at the close of the season. In a cooperative this is cared for automatically through the return of savings. With a noncooperative additional testing may be required. 3. That the samples taken in 1967 are representative of the type of variation encountered in other years or under other conditions. 4. That no bias occurred in sampling procedures. 5. That nuts are clean, whether on a green weight or dry weight basis. 6. That the relative value of nuts per pound is known for each size class and remains essentially the same. Analysis: Accuracy of the Steinlite Tester: The estimate of percent moisture for green nuts, as determined by the Steinlite Tester, is compared to a calculated percent moisture, as obtained from oven-dried weights, for each lot in Table I (Appendix). The percent moisture was calculated as 100 times the ratio of the weight of the moisture contained in the sampled green nuts to the total weight of the green nuts. If W = the desiccated weight of the sampled nuts M1 = the weight of the moisture in the dried sample nuts M2 = the weight of the moisture lost in the drying process the recorded data contain --- W + M 1 = the weight of the dried sampled nuts W + M 1 + M2 = the weight of the green sampled nuts 100 Mi W + Mi - the percent moisture of the dried nuts, a Steinlite reading.
5 -4- The calculated percent moisture of green nuts, 100 M 1 + M2 W + M 1 M2 was obtained from the recorded data using the following relationships for estimates of M i and M2. M i = W + M)(100 M 1Weight of the Dried Sampled Nuts 100 times Steinlite Reading ( 100 W + M1 M2 = (W + M 1 + M2 ) - (W + M 1) = (Weight of Green Sampled Nuts) - (Weight of Dried Sampled Nuts) From Table I of the Appendix, the mean value of the sample lots using the Steinlite readings was 3.3 percent greater than the calculated procedure. This would indicate that the Steinlite Tester does not account for the total moisture content in the green sample but is sufficiently accurate for this type of measurement. Shrinkage from Drying: The average green nut size, measured in 64ths of an inch, is compared to the average dried nut size for each lot in Table II. The mean decrease in nut size, from drying, is ths of an inch. The average sizes of the various classes of filberts were taken to be 42.0 for baby, 47.0 for medium, 52.5 for large, 57.0 for jumbo, and 62.0 for giant. The average green nut sizes from Table II were divided into six size classifications to show the distribution by size and the corresponding shrinkage after drying. Table III indicates that shrinkage is uniform with size. Defective Nuts at Green and Dried Stages: The average percent of blank, wormy, and shriveled green nuts is compared to the average percent of blank, wormy, and shriveled dried nuts for each lot
6 in Table IV. Tests of significance were performed to determine differences between green and dried nuts. The percent of blank and shriveled nuts was found to be significantly (P<;.01) greater for dried nuts than for green nuts. Basis of Payment to the Growers: The price per pound paid to the grower can be based on samples of either green or dried nuts. From either kind of sample, the relative number of nuts in each size class, the percent of blank nuts, and the percent moisture of the nuts in a lot can be estimated. The following values were assumed for all calculations. The number of nuts per pound were determined from a relatively small industry sample, and although it may have some error, the relative values appear reasonable. The analysis is not particularly sensitive to changes in either number of nuts per pound or market value per pound so long as the relative values remain consistent. DRIED NUTS Size Class Market Value/Pound No. of Nuts/Pound Market Value/Nut Baby Medium Large Jumbo-Giant 23.63* Market Value/Pound No. of Nuts/Pound = Market Value/Nut, e.g T 203 =.07
7 -6-1. The lot value, based only on nut sizes, of a dried sample was calculated as follows: = (.07) (No. of Baby Nuts).12) (No. of Medium Nuts) (.16) (No. of Large Nuts) (.23) (No. of Jumbo-Giant Nuts) The weight of the sample = No. of baby nuts/203 + No. of medium nuts/171 No. of large nuts/137 + No. of jumbo-giant nuts/102.5 The price per pound of dried nuts, based only on nut size, is given by: P DS = VDS 1 - blanks _.05) \ 100 For example, if a grower's sample registers ten percent blanks, and assuming Pm of dried nuts is 20.00, then P will be: DSB PDSB = [r ] 100 = El - ( )] = [ 1 - (.05)] = I.951 = Drying samples of filberts is expensive and time consuming; therefore, the price per pound was also calculated from green sample data. GREEN NUTS Size Class Market Value/Pound No. of Nuts/Pound Market Value/Nut Baby x K.06 /K Medium x K.10 /K Large x K.13 /K Jumbo-Giant x K.19 /K
8 -7- Market Value/Pound of green nuts, shown in the above table, is 84.36% of the corresponding value for dried nuts. This percentage was determined from 1967 data. The "K" appearing in the table is the proportionality factor resulting from the assumption that No. of Nuts/Pound and Market Value/Nut are proportional to the corresponding values for dried nuts. by: Therefore, the value of a green sample, based only on nut sizes, is given 6) (No. of Baby Nuts) (.10) (No. of Medium Nuts) K / 3 (No. of Large Nuts) +(.19' (No. of Jumbo-Giant Nuts) K The weight of the sample = No. of Baby Nuts + No. of Medium Nuts 203 x K 171 x K and + No. of Large Nuts + No. of Jumbo-Giant Nuts 137 x K x K = VGs/weight of the sample Note that the factor K is common to every term in both the numerator and the denominator of P GS Consequently, the value of K cancels out and does not need to be known. As in the case of dried samples, percent blanks among green nuts can be taken into account. P GSB = P GS 1 - (% blanks In order to avoid sizing sampled dried nuts, the price per pound based only on percent blanks can be determined, if an average market price for all sizes PD is assumed. DB = P D [1 -( blanks -.05)] 100
9 -8-4. If green samples are used, however, percent moisture must be considered. Data from 1967 was used to establish the relationship between the percent moisture of green nuts and weight lost in the drying process. Moisture after drying = 36.77% of moisture of green nuts. The allowable percent moisture of marketable nuts was assumed to be 10%. Therefore, the modifying factor for moisture is: [ (% moisture of green nuts - 10)] 100 If an average market price per pound for all sizes of green filberts is called P, then the price per pound to be paid to the grower, based on percent G blanks and percent moisture of green sampled nuts, is given by: moisture -.10) P GBM = PG G blanks The following example is given to illustrate the derivation of price per pound based on blanks and moisture considerations. Assume: percent blanks in sample percent moisture content of green nuts 3. P G equals P = ( )J [ ( )] GBM [ = [1 - ( )][l ( )] = [1 - (.05)] Cl- (.06)] = ] V.94 = [.88] = 17.60$
10 _9_ Sample Size Required to Obtain Given Levels of Precision in Estimating Price Estimates of the coefficient of variation of P P P and DSB' GSB' DB' P GBM were calculated from the 1967 data. Basis C. V. (%) DSB 7.43 GSB 6.04 DB 7.38 GBM 6.22 The following equation was used to determine the number of samples needed to attain specified levels of precision. n = t2 (C.V.)2 P 2 where n = number of samples of 50 nuts each t = 1.645, the value of Student's - t associated with 90% confidence C. V. = coefficient of variation p = percent precision desired Number of Samples Required p (±%) DSB GSB DB GBM If 95 percent confidence were desired, n, the number of samples would have to be increased by 41 percent. The concern for determining the number of samples to be taken is, important because it is desirable for both the grower and buyer to have a
11 -10- good representation of the entire quantity offered by the grower. Statistically, concern is given that the sample size, or number of samples taken, is large enough to be a good representative of the total quantity. One sample of 50 nuts may have 40% baby nuts, when the entire quantity of nuts, if all were sized, might have only 20% baby nuts. By taking more samples, a better estimate of the total can be made. The objective is to take as few samples as possible and still have enough nuts to meet the desired level of precision. By using the above equation, the number of samples of 50 nuts each was determined to give estimates of the prices per pound of filbert within specified limits. For example, by taking seven samples of each lot, the price of green nuts per pound with allowances for blanks and moisture content, P will be within four percent of the true price 90 percent of the time. GBM' The number of samples is more important than the size of samples. The 1967 data indicate that the price per pound on a green weight basis is approximately 84% of the price per pound on a dry weight basis. (See Figure 1.) This means that if a firm wanted to pay out or return to the grower members the same number of dollars as it did in 1966 when buying on a dry weight basis, the green weight price per pound would be about 84% of the dry weight price per pound. Conclusion: From the preceding analysis, the following conclusions were reached: 1. The number of samples required to obtain given levels of precision in estimating prices per pound of filberts is dependent upon the confidence level desired. For instance, if a confidence level of 90 percent* is desired, it would be necessary to take the
12 following number of samples from each lot of nuts: Sample size for 90 percent Limits of Precision (±%) confidence * Confidence level of 90 percent = 90% of the time true value will be within specified limits of precision. 2. The Steinlite Tester is quite accurate. The estimate of moisture loss was about the same when calculated from a dry weight basis or determined by Steinlite Tester. 3. The shrinkage from drying is uniform among the various sizes. The mean shrinkage was ths of an inch or 1.6 percent. 4. The percentage of blanks and shriveled nuts was greater in the dry samples than in the green samples. This could be a problem! 5. Using the size of nuts to determine payment is NOT necessary. There existed an extremely high correlation (.993) between prices paid based on dry weight and percent blank and prices based on weight by size classes and percent blank. The prices were essentially equivalent. 6. The results of this 1967 study indicate that the price per pound on a green weight basis is approximately 84 percent of the price per pound on a dry weight basis.
13 -14- Table I Percent Moisture in Green Filberts Lot Steinlite Reading Calculated % Moisture MEAN % difference
14 -15- Table II Average Nut Size in 64ths of an Inch Lot Green Dried Decrease MEAN (1.6%)
15 -1n- Table III Decrease in Nut Size from Drying Green nut size Mean decrease No. of lots
16 Table IV -17- Percents Defective Filberts Lot Green Percent Blank Dried Difference Green Percent Wormy Dried Difference Percent Shriveled Green Dried Difference MEAN
17 Table V -18- Characteristics of Sampled Filberts Standard Percent Weight of Percent of Percent Weight of Percent of price moisture of 50 green blank green moisture of 50 dried blank dried per lb. green nuts nuts nuts dried nuts nuts nuts i MEAN
18 -19- MOD.111 I I N 0 01 c0 <0 LO :t (0 N CVN C N33b0 ) annod 83c1 3D1licl I
19 FILBERT SAMPLING AND TESTING EVALUATION (Barcellona Variety only) I. Purpose and objectives: 1. To evaluate current buying practices. 2. To measure degree of precision of sampling procedure. 3. To recommend possible alternative sampling procedures. 4. To compare moisture determination by Steinlite Tester with regular drying method. 5. To compare sizing of green and dry nuts. II. Procedures: 1. Draw samples from 50 lots. a. Five (5) lots each day for 10 days. b. Sample No lots with less than 2,000 pounds. c. For the 5 lots each day, select the first 5 lots, with 2,000 pounds or more, received after 10 a.m. 2. Draw one representative sample* per 1,000 pounds and then draw one representative sample per each additional 2,000 pounds for the balance of the load. Use the 50 nut crack test and record on special forms provided by OSU. 3. Moisture will be run on Steinlite Tester and percentage recorded on special forms provided by OSU. 4. Size testing will be done for each nut in the 50 nut crack sample and each size will be recorded separately on the special forms provided by OSU. 5. Number of blanks, worms, and shrivels will also be separately recorded on special forms provided by OSU. 6. The remainder of the representative sample will be dried under normal conditions and used as a check (Green vs. Dried). * Representative Sample = 3 pound box secured as nuts are received at dumping station.
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